Problem: If $a + b + c = 2$ and $x + y + z = 6$, what is $4a + 4c - 9y - 9z - 9x + 4b$ ?
$= 4a + 4b + 4c - 9x - 9y - 9z$ $= (4) \cdot (a + b + c) + (-9) \cdot (x + y + z)$ $= (4) \cdot (2) + (-9) \cdot (6)$ $= 8 - 54$ $= -46$